If x + (1/x) = 2 cos θ, then for any integer n, xn + (1/xn) =

Question

If x + (1/x) = 2 cos θ, then for any integer n, xn + (1/xn) =  (A) 2 cos nθ (B) 2 sin nθ (C) 2i cos nθ (D) 2i sin nθ

Tardigrade Admin · Accepted Answer

Let x= cos θ+i sin θ Then, (1/x)= cos θ-i sin θ ∴ x+(1/x)=2 cos θ ⇒ xn+(1/xn)=2 cos n θ

Q. If $x + \frac{1}{x} = 2 cos θ$ , then for any integer $n$ , $x^{n} + \frac{1}{x ^{n}} =$